cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A034825 Number of n-node rooted trees of height at most 8.

Original entry on oeis.org

1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 718, 1832, 4702, 12159, 31515, 81888, 212878, 553557, 1438741, 3737331, 9700188, 25156049, 65181067, 168746672, 436505846, 1128256918, 2914103577, 7521450053, 19400577711, 50010551503, 128841990772, 331754004302
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

See A001383 for details.

Programs

  • Maple
    For Maple program see link in A000235.
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: shr:= proc(p) n->`if`(n=0, 1,p(n-1)) end: b[0]:= etr(n->1): for j from 1 to 6 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[6]): seq(a(n), n=0..31); # Alois P. Heinz, Sep 08 2008
  • Mathematica
    Prepend[Nest[CoefficientList[Series[Product[1/(1-x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x]&, {1}, 8], 1] (* Geoffrey Critzer, Aug 01 2013 *)

Formula

Take Euler transform of A034824 and shift right. (Christian G. Bower).

A000418 Number of n-node rooted trees of height 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 7, 34, 136, 487, 1615, 5079, 15349, 45009, 128899, 362266, 1002681, 2740448, 7411408, 19865445, 52840977, 139624510, 366803313, 958696860, 2494322662, 6463281890, 16686206047, 42935345688, 110142163940, 281763465941
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column h=7 of A034781.

Programs

  • Maple
    For Maple program see link in A000235.
  • Mathematica
    b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1 || k < 1, 0, Sum[ Binomial[b[i - 1, i - 1, k - 1] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 7] - b[n - 1, n - 1, 6]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *)

Formula

A034824-A034823. - Christian G. Bower

A000429 Number of n-node rooted trees of height 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 43, 188, 728, 2593, 8706, 27961, 86802, 262348, 776126, 2256418, 6466614, 18311915, 51334232, 142673720, 393611872, 1078955836, 2941029334, 7977065816, 21541492856, 57942770689, 155304829763, 414934057486
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column h=8 of A034781.

Programs

  • Maple
    For Maple program see link in A000235.
  • Mathematica
    b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1 || k < 1, 0, Sum[ Binomial[b[i - 1, i - 1, k - 1] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 8] - b[n - 1, n - 1, 7]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *)

Formula

a(n) = A034825(n) - A034824(n). - Christian G. Bower
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.